Piecewise linear approximation of smooth functions of two variables

Joseph H.G. Fu

doi:10.5802/acirm.51

Joseph H.G. Fu ¹

¹ Department of Mathematics University of Georgia Athens GA 30602 USA

Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 11-16.

Abstract

The normal cycle of a singular subset $X$ of a smooth manifold is a basic tool for understanding and computing the curvature of $X$ . If $X$ is replaced by a singular function on $ℝ^{n}$ then there is a natural companion notion called the gradient cycle of $f$ , which has been introduced by the author and by R. Jerrard. We discuss a few fundamental facts and open problems about functions $f$ that admit gradient cycles, with particular attention to the first nontrivial dimension $n = 2$ .

Published online: 2014-11-12

DOI: 10.5802/acirm.51

Classification: 00X99
Keywords: graph theory, shape recognition, optimal transportation

Author's affiliations:

Joseph H.G. Fu ¹

¹ Department of Mathematics University of Georgia Athens GA 30602 USA

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Joseph H.G. Fu. Piecewise linear approximation of smooth functions of two variables. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 11-16. doi : 10.5802/acirm.51. https://acirm.centre-mersenne.org/articles/10.5802/acirm.51/

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